Question

An airplane is heading due south at a speed of 600 km h. If a wind begins blowing from the
southwest at a speed of 100 km h (average), calculate: (a) the velocity (magnitude and direction) of the plane relative to the ground

Answer 1

Please keep in mind the wind is blowing FROM the southwesterly direction, not towards.

Answer 2

I got the answer, but thanks anyways! :)

Answer 3

Here's what I got:

Let's assume that N and E are + directions while S and W are - directions.

Wind is blowing from SW; thus, it is blowing towards NE (or at 45 deg N of E).

Dividing the wind's speed into components:
y-component: +70.71 km/h; x-component: +70.71 km/h

Dividing the airplane's speed into components:
y-component: -600 km/h; x-component: 0 km/h

Adding the components to get the resulting components:
y-component: -529.29 km/h; x-component: +70.71

Using the Pythagorean Theorem to find the resulting speed:
v^2 = y^2 + x^2 so v = 533.99 km/h

To find the angle of direction, use arctan (y/x):
arctan (529.29/70.71) = 82.39 deg

ANSWER: velocity = 533.99 km/h at 82.39 deg S of E